(-4k^4+14*3k^2)+(-3k^4-14k^2-8)=

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Solution for (-4k^4+14*3k^2)+(-3k^4-14k^2-8)= equation:


Simplifying
(-4k4 + 14 * 3k2) + (-3k4 + -14k2 + -8) = 0

Multiply 14 * 3
(-4k4 + 42k2) + (-3k4 + -14k2 + -8) = 0

Reorder the terms:
(42k2 + -4k4) + (-3k4 + -14k2 + -8) = 0

Remove parenthesis around (42k2 + -4k4)
42k2 + -4k4 + (-3k4 + -14k2 + -8) = 0

Reorder the terms:
42k2 + -4k4 + (-8 + -14k2 + -3k4) = 0

Remove parenthesis around (-8 + -14k2 + -3k4)
42k2 + -4k4 + -8 + -14k2 + -3k4 = 0

Reorder the terms:
-8 + 42k2 + -14k2 + -4k4 + -3k4 = 0

Combine like terms: 42k2 + -14k2 = 28k2
-8 + 28k2 + -4k4 + -3k4 = 0

Combine like terms: -4k4 + -3k4 = -7k4
-8 + 28k2 + -7k4 = 0

Solving
-8 + 28k2 + -7k4 = 0

Solving for variable 'k'.

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
1.142857143 + -4k2 + k4 = 0

Move the constant term to the right:

Add '-1.142857143' to each side of the equation.
1.142857143 + -4k2 + -1.142857143 + k4 = 0 + -1.142857143

Reorder the terms:
1.142857143 + -1.142857143 + -4k2 + k4 = 0 + -1.142857143

Combine like terms: 1.142857143 + -1.142857143 = 0.000000000
0.000000000 + -4k2 + k4 = 0 + -1.142857143
-4k2 + k4 = 0 + -1.142857143

Combine like terms: 0 + -1.142857143 = -1.142857143
-4k2 + k4 = -1.142857143

The k term is -4k2.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4k2 + 4 + k4 = -1.142857143 + 4

Reorder the terms:
4 + -4k2 + k4 = -1.142857143 + 4

Combine like terms: -1.142857143 + 4 = 2.857142857
4 + -4k2 + k4 = 2.857142857

Factor a perfect square on the left side:
(k2 + -2)(k2 + -2) = 2.857142857

Calculate the square root of the right side: 1.690308509

Break this problem into two subproblems by setting 
(k2 + -2) equal to 1.690308509 and -1.690308509.

Subproblem 1

k2 + -2 = 1.690308509 Simplifying k2 + -2 = 1.690308509 Reorder the terms: -2 + k2 = 1.690308509 Solving -2 + k2 = 1.690308509 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + k2 = 1.690308509 + 2 Combine like terms: -2 + 2 = 0 0 + k2 = 1.690308509 + 2 k2 = 1.690308509 + 2 Combine like terms: 1.690308509 + 2 = 3.690308509 k2 = 3.690308509 Simplifying k2 = 3.690308509 Take the square root of each side: k = {-1.921017571, 1.921017571}

Subproblem 2

k2 + -2 = -1.690308509 Simplifying k2 + -2 = -1.690308509 Reorder the terms: -2 + k2 = -1.690308509 Solving -2 + k2 = -1.690308509 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + k2 = -1.690308509 + 2 Combine like terms: -2 + 2 = 0 0 + k2 = -1.690308509 + 2 k2 = -1.690308509 + 2 Combine like terms: -1.690308509 + 2 = 0.309691491 k2 = 0.309691491 Simplifying k2 = 0.309691491 Take the square root of each side: k = {-0.556499318, 0.556499318}

Solution

The solution to the problem is based on the solutions from the subproblems. k = {-1.921017571, 1.921017571, -0.556499318, 0.556499318}

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